Hello,
for fans of sudoku's, I propose a site which presents giant sudoku's (size 16x16, 25x25, .... up to 100x100 sudoku's), wordokus and interactive puzzles. The site is a french personal site (sudokugeant), but the puzzles are universal.

Well, this example is almost trivial (apart from its size). It can be solved completely by singles and, even sticking only to singles, it is very far from minimal. The version below is yours with 1155 clues removed and is locally minimal using only singles. If you remove certain clues further, e.g. the 39 at r10c100, you get a valid puzzle that requires more refined techniques

I hope you find these comments useful. Work on massive puzzles seems to have peaked about three years ago when they were on a suduko frontier. I think most people now regard them as, at best, a curiosity. Pity really, I did quite a lot of work on my program to be able to handle these giants.

Hello.
I have checked the grid without the “39” in r10c100. The solver found the solution in 10h21min with 4 algorithms : AL1 x 24044 + AL2 x 7719 + AL3 x 2011 + AL4 x 825 (*) ! So, this puzzle can be qualified as mega-evil (at least) ….
(*) With the “39”, the time to solve the grid is 12min with 2 algo (AL1 x 893 + AL2 x 337).
AL4 explores a binary tree and the average depth of the tree is 18. To avoid an excessive duration, I have stopped the solver after the solution was found, and the post-solution branches have not been explored ! So unfortunately, I have not proved that this solution is unique.
Anyway, it was a very interesting exercise ! Congratulations for your work, Mike.
Phil.

I have checked the grid without the “39” in r10c100. The solver found the solution in 10h21min with 4 algorithms : AL1 x 24044 + AL2 x 7719 + AL3 x 2011 + AL4 x 825 (*) ! So, this puzzle can be qualified as mega-evil (at least) ….
(*) With the “39”, the time to solve the grid is 12min with 2 algo (AL1 x 893 + AL2 x 337).
AL4 explores a binary tree and the average depth of the tree is 18. To avoid an excessive duration, I have stopped the solver after the solution was found, and the post-solution branches have not been explored ! So unfortunately, I have not proved that this solution is unique.

Phil,

Your program does seem to be rather on the slow side: mine solves the two variations of your puzzle in 25s and 20s, respectively. Are you using an interpreted language?

You might like to look too at the two puzzles I posted here. They took about a day to generate but need only 100s to solve, using logic only.

Mike,
I have just tried your grids. I am extremely sorry, but I give up ! Your grids are too complex for my solver. It enters again a tree-search, which will be probably too long.
(The solver is written in visual basic and runs on Windows Vista).
phil.

This is probably one cause. These massive problems need a high-performance language, close to the hardware and highly optimized. As far as I understand, most work in this area is done in C, although I personally use Fortran 95 with the highly-optimizing Intel compiler. This gives access to an array language. As an example, the code for naked singles is just

where you will note that it is independant of the problem size (rank2); count and maxloc are intrinsic functions. The procedure update updates the pencil marks.

But aside from that, you appear to be too readily giving up on logic. You can prune the search tree, or even avoid a search altogether, by adding code for hidden and naked pairs and triplets, and for pointing.

Hi Mike !
As you have suggested, I have added logic routines to improve my solver (but always in Visual Basic).
Now, the “without 39” grid is solved in “only” 14 minutes.
I have also checked your grids. I do confirm that they are much more difficult ! The 6264 grid is solved in 5,8 hours (!) and the 5891 grid in 7,3 hours (!!).
I would like to know if these grids are the most complex you can generate or if it is possible to create still more complex grids ?
Regards.
phil